Lecture Notes on Sobolev Spaces
نویسنده
چکیده
We denote by Lloc(IR) the space of locally integrable functions f : IR 7→ IR. These are the Lebesgue measurable functions which are integrable over every bounded interval. The support of a function φ, denoted by Supp(φ), is the closure of the set {x ; φ(x) 6= 0} where φ does not vanish. By C∞ c (IR) we denote the space of continuous functions with compact support, having continuous derivatives of every order. Every locally integrable function f ∈ Lloc(IR) determines a linear functional Λf : C∞ c (IR) 7→ IR, namely Λf (φ) . = ∫
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